A335902 Composite numbers c such that phi(c)/phi(mind(c)) mod phi(c)/phi(maxd(c)) <> 0, where phi is the Euler function, mind(c) is the smallest nontrivial divisor of c, maxd(c) is the largest nontrivial divisor of c.

35, 55, 77, 95, 115, 119, 143, 155, 161, 187, 203, 209, 215, 221, 235, 245, 247, 253, 287, 295, 299, 319, 323, 329, 335, 355, 371, 377, 391, 395, 403, 407, 413, 415, 437, 473, 493, 497, 515, 517, 527, 533, 535, 551, 559, 581, 583, 589, 605, 611, 623, 629, 635, 649

Offset

1,1

Comments

This equivalence criterion splits a set of composite numbers into two classes and can be used to count certain combinatorial objects.

Links

Table of n, a(n) for n=1..54.

Prog

(MATLAB)
n=500; % gives all terms of the sequence not exceeding n
A=[];
for i=1:n
    dn=divisors(i);
    if size(dn, 2)>2 && mod (totient(i)/totient(dn(2)), totient(i)/totient(dn(end-1)))~=0
        A=[A i];
    end
end
function [res] = totient(n)
res=0;
    for i=1:n
        if gcd(i, n)==1
            res=res+1;
        end
    end
end
(PARI) isok(c) = if ((c>1) && !isprime(c), my(t=eulerphi(c), d=divisors(c)); ((t/eulerphi(d[2])) % (t/eulerphi(d[#d-1]))) != 0); \\ Michel Marcus, Dec 28 2020

Crossrefs

Cf. A000010, A002808, A340058.

Sequence in context: A318572 A171082 A340269 * A121707 A267999 A319386

Adjacent sequences: A335899 A335900 A335901 * A335903 A335904 A335905

Keyword

nonn

Author

Maxim Karimov, Dec 28 2020

Status

approved